Legal Question in Personal Injury in Georgia

We don't know since you omitted most of the story. In addition, "responsible" for what? If the other child came out of nowhere and hit your child, the other child's parents are generally liable for injuries, medical bills. If your child started something and the other child was protecting him/her self, you probably need to cover the expenses (and perhaps the expense of the other child). Something else ... who knows. You need facts.